An Alternative Approach to Lie Groups and Geometric Structures

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Ercüment H. Ortaçgil (Professor Emeritus, Professor Emeritus, Bogazici University)

An Alternative Approach to Lie Groups and Geometric Structures

Ercüment H. Ortaçgil (Professor Emeritus, Professor Emeritus, Bogazici University)

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English

Oxford University Press
26 July 2018

Mathematics; Geometry; Algebraic geometry

This book presents a new and innovative approach to Lie groups and differential geometry. Rather than compiling and reviewing the existing material on this classical subject, Professor Ortaçgil instead questions the foundations of the subject, and proposes a new direction.

Aimed at the curious and courageous mathematician, this book aims to provoke further debate and inspire further development of this original research.

By: Ercüment H. Ortaçgil (Professor Emeritus Professor Emeritus Bogazici University)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Dimensions: Height: 240mm, Width: 163mm, Spine: 17mm
Weight: 1g
ISBN: 9780198821656
ISBN 10: 0198821654
Pages: 228
Publication Date: 26 July 2018
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Fundemental concepts 1: Parallelizable manifolds 2: The nonlinear curvature 3: Local Lie Groups (LLG.s) 4: The centralizer 5: s-invariance 6: The linear curvature 7: The structure object Some Consequences 8: The nonlinear Spencer sequence 9: Deformations 10: The de Rham cohomology of a LLG 11: The linear Spencer sequence 12: The secondary characteristic classes 13: The homogeneous flow 14: The Van Est Theorem 15: The symmetry group How to Generalize 16: Klein geometries 17: The universal jet groupoids 18: Embeddings of Klein geometries into universal jet groupoids 19: The de.nition of a prehomogeneous geometry (PHG) 20: Curvature and generalized PHG.s

Professor Ercüment Ortaçgil received his PhD from Johns Hopkins University in 1985, and then returned home to Turkey to join the mathematics department at Bogazici University, Istanbul. He retired in 2011, and set his mind to the writing this book to inspire further research on the seemingly elementary problems that have enamoured him throughout his career.

Reviews for An Alternative Approach to Lie Groups and Geometric Structures

In this very nice and unusual book, the author proposes an alternative approach to the theory of Lie groups, together with some applications and generalization of it. The approach proposed is inspired by the geometric theory of partial differential equations (PDEs) and Lie pseudogroups. In this respect, it is much closer in spirit to the original works of Lie and Klein than the current modern theory...The book is suitable for students at a master's level. * Luca Vitagliano, American Mathematical Society *